Thanks for the help everyone. Had some time to work on this today and I got the progmem stuff working, no issues holding the data set or going back and forth from RAM to flash memory.
I did use the Flash library - Flash | Arduiniana
That made interfacing with flash memory way easier and more intuitive, I'd recommend it highly.
I also got my data from Excel into Arduino. I did it without any programming, this was my method:
I realized I had the data ready to go in CSV, the speed bump in my brain was the fact that each array's values was a column and not a row. So I would have to parse the line breaks and fill each array sequentially from the CSV which I didn't know how to do. I realized this didn't have to be the case. All I did was copy the columns of data in Excel and paste special, transpose, into a new workbook, so now they're rows instead of columns. Then saved as CSV. Then opened in a text editor. Then I just had to copy each line and it was a nice already formatted array of data with commas so I just paste each line (4 total) into the IDE. I just used a one dimensional array per variable (instead of what I was thinking before of a single 2 dimensional array holding all the variables). This way it just took me two minutes tops to get it into Arduino, without programming. Didn't even need curly brackets with this particular library.
So now my final step is tightening up the timing. Right now I'm using delays but I need the values to change exactly at the right time without worrying about how long processing took. So I'm going to use the Elapsed Millis library, just need to sit down and figure out how to do it.
Thanks again for the help, would have taken me much longer to get this far without it!